What's weird in the Stern-Gerlach experiment?

The first thing is that it gets discrete spin states. Ok so we filter out a spin up state |+> and then send it through a perpendicular Apparatus then act surprised that we got |-> states back, isn't that what precession does? the only weird thing I can think of is that even after precession we still get discrete states (classically they should get rotated continuously even if they started with certain discrete values).

There are only two real life numbers we can get, [itex]\hbar /2,-\hbar /2[/itex], no matter what. If we select for [itex]|\uparrow\rangle[/itex], then with the selected beam send it through a perpendicular apparatus the new states are [itex]|\psi\rangle=1/\sqrt{2}(|\uparrow\rangle+|\downarrow\rangle )[/itex], meaning we can get 50/50 spin up/down. Does that help?

Firstly you get discrete spin states in equal number (using a random source).
This differs from what would happen if spin were classical angular momentum (and corresponding magnetic moment) about an arbitrary axis. If you take say those toy magnetic spheres (Zen magnets or Nanodot magnets) and shoot them out a BB gun through an SG magnet you'll get a continuous spread of deflections.

So if you try to explain this in terms of the SG magnets pulling the classical spin directions into line no scheme will agree with the proportion of discrete outcomes you see when you do two SG experiments in succession at different angles.

This verifies that the intrinsic spin is intrinsically a quantum mechanical phenomenon and not simply accidental quantization of a classical situation.

Further when you use spin 1, spin 3/2, spin 2,... composite particles you will get the QM predicted discrete deflections.

What is nice about the SG experiment is you can (relatively) easily carry it out on one particle at a time. This is very difficult to do with photons and polarization experiments. It's damned difficult to create a device which emits exactly 1 photon on demand. (The elusive photon gun).

Stern-Gerlach experiment can be used to demonstrate that spin in z-direction can be influenced by a measurement of spin in y-direction. Weird enough?

yes, but classically it gets influenced too, because the magnetic moment rotates around the direction of the magnetic field.

but i think I got it now: the z-direction only got influenced when you blocked states, so you can pass the beam through a y-direction magnet and not block any state (don't measure the spin) the result is that you didn't change the state, so we know the magnet didn't do it, its the act of measurement that did.